Chapter 10.5, Problem 72E

a.

To determine

To calculate:

Probability that you are chosen to be first or second presenter on first day.

Answer to Problem 72E

Probability that you are chosen to be first or second presenter on first day is $0.5$ .

Explanation of Solution

Given information:

Each day $4$ students makes their presentations in order chosen at random by the teacher.

Calculation:

The number of possible outcomes as the number of combinations of $4$ students taken $1$ at a time $C{}_1$ because order is not important.

The expression for combination for $n$ objects $r$ at a time is given by,

  $C{}_r=\frac{n!}{\left(n-r\right)!.r!}$

The required numbers of combinations are as below,

  $\begin{array}{l}C{}_1=\frac{4!}{\left(4-1\right)!.1!}\\ C{}_r=\frac{4.3!}{3!.1}\\ C{}_r=4\end{array}$

To find the favorable outcomes.

Now it is essential to find out the probability that person concerned is chosen first or second presenter on first day.

To find out probability,

  $P$ (first or second presenter),

  $\begin{array}{l}=\frac{1}{4}+\frac{1}{4}\\ =\frac{2}{4}\\ =\frac{1}{2}\end{array}$

Thus, answer is $0.5$ .

b.

To determine

To calculate:

Probability that you are chosen to be second or third presenter on first day.

Answer to Problem 72E

Probability that you are chosen to be second or third presenter on first day is $0.5$ .

Explanation of Solution

Given information:

Each day $4$ students makes their presentations in order chosen at random by the teacher.

Calculation:

The number of possible outcomes as the number of combinations of $4$ students taken $1$ at a time $C{}_1$ because order is not important.

The expression for combination for $n$ objects $r$ at a time is given by,

  $C{}_r=\frac{n!}{\left(n-r\right)!.r!}$

The required numbers of combinations are as below,

  $\begin{array}{l}C{}_1=\frac{4!}{\left(4-1\right)!.1!}\\ C{}_r=\frac{4.3!}{3!.1}\\ C{}_r=4\end{array}$

To find the favorable outcomes.

Now it is essential to find out the probability that person concerned is chosen second or third presenter on first day.

To find out probability,

  $P$ ( second or third presenter),

  $\begin{array}{l}=\frac{1}{4}+\frac{1}{4}\\ =\frac{2}{4}\\ =\frac{1}{2}\end{array}$

Thus, answer is $0.5$ .